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729 liters of a mixture contains milk and water in the ratio 7:2.

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729 liters of a mixture contains milk and water in the ratio 7:2.  [#permalink]

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New post 20 Mar 2019, 23:44
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729 liters of a mixture contains milk and water in the ratio 7:2. How much water must be added to get a new mixture containing milk and water in the ratio 7:3?

A. 100 liters
B. 81 liters
C. 72.9 liters
D. 90 liters
E. 50 liters

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Re: 729 liters of a mixture contains milk and water in the ratio 7:2.  [#permalink]

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New post 26 Mar 2019, 06:20
(162 + x)/(729+x) = .3 solving for x we get 81. Hence option B

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Re: 729 liters of a mixture contains milk and water in the ratio 7:2.  [#permalink]

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New post 26 Mar 2019, 10:48
DisciplinedPrep wrote:
729 liters of a mixture contains milk and water in the ratio 7:2. How much water must be added to get a new mixture containing milk and water in the ratio 7:3?

A. 100 liters
B. 81 liters
C. 72.9 liters
D. 90 liters
E. 50 liters


given water ; 729 * 2/9 ; 162 and milk = 567
so required ratio 3:7 ; 3/10
so milk to be added 162+x/729+x = 3/10
solve for x = 81
IMO B
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Re: 729 liters of a mixture contains milk and water in the ratio 7:2.  [#permalink]

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New post 13 Apr 2019, 19:15
DisciplinedPrep wrote:
729 liters of a mixture contains milk and water in the ratio 7:2. How much water must be added to get a new mixture containing milk and water in the ratio 7:3?

A. 100 liters
B. 81 liters
C. 72.9 liters
D. 90 liters
E. 50 liters


#Work-Backwards Strategy
If Milk:Water is 7:2 in 729 Liters, then milk is 567 Liters.
Final mixture is 729+x liters (x liters of water added)

Option D (x=90)
Final amount of milk: (729+90)*7/10 does not equal 567 Liters of Milk.
Skip Option D.

Option B (x=81)
Final amount of milk: (729+81)*7/10 equals 567 Liters of Milk.
Option B is the right Answer.
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Re: 729 liters of a mixture contains milk and water in the ratio 7:2.  [#permalink]

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New post 24 Jun 2019, 08:32
DisciplinedPrep wrote:
729 liters of a mixture contains milk and water in the ratio 7:2. How much water must be added to get a new mixture containing milk and water in the ratio 7:3?

A. 100 liters
B. 81 liters
C. 72.9 liters
D. 90 liters
E. 50 liters


m:w :: 7/3 = {(7/9)*729 }/ {(2/9)*729 + x}
We have to find x liters of added water.
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Re: 729 liters of a mixture contains milk and water in the ratio 7:2.  [#permalink]

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New post 24 Jun 2019, 09:12
20.........90
......27.....
63..........7

Water needs to be added=(7/63)*729=81


DisciplinedPrep wrote:
729 liters of a mixture contains milk and water in the ratio 7:2. How much water must be added to get a new mixture containing milk and water in the ratio 7:3?

A. 100 liters
B. 81 liters
C. 72.9 liters
D. 90 liters
E. 50 liters


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Re: 729 liters of a mixture contains milk and water in the ratio 7:2.  [#permalink]

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New post 24 Jun 2019, 09:28
DisciplinedPrep wrote:
729 liters of a mixture contains milk and water in the ratio 7:2. How much water must be added to get a new mixture containing milk and water in the ratio 7:3?

A. 100 liters
B. 81 liters
C. 72.9 liters
D. 90 liters
E. 50 liters


Qty of water = 2/9*729 = 162 liters
Qty of milk = 729 - 162 = 567 liters

Let the water be added = x liters
Total volume = (729 + x) liters

Milk : Water = 7 : 3
Fraction of milk = 7/10
—> 567/(729 + x) = 7/10
—> 81/(729 + x) = 1/10
—> 810 = 729 + x
—> x = 81 liters

IMO Option B

Pls Hit kudos if you like the solution

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Re: 729 liters of a mixture contains milk and water in the ratio 7:2.   [#permalink] 24 Jun 2019, 09:28
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